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9780495012726

Nature of Mathematics (with CengageNOW and Personal Tutor Printed Access Card)

by
  • ISBN13:

    9780495012726

  • ISBN10:

    0495012726

  • Edition: 11th
  • Format: Hardcover
  • Copyright: 2006-09-29
  • Publisher: Brooks Cole
  • View Upgraded Edition

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Supplemental Materials

What is included with this book?

Summary

Experience mathematics and hone your problem-solving skills with THE NATURE OF MATHEMATICS and its accompanying online learning tools. The author introduces you to Polya's problem-solving techniques and then shows you how to use these techniques to solve unfamiliar problems. You'll also find coverage of historical topics, and exercise sets that feature problems applied to real world settings. Included with your purchase is access to the ThomsonNOW, an online tutorial that allows you to work with real math notation in real time, with unlimited practice problems, instant analysis and feedback, and streaming video to illustrate key concepts, as well as vMentor, a live, online mathematics tutoring service.

Table of Contents

Prologue: Why Math? A Historical Overview 1
The Nature of Problem Solving
1(50)
Problem Solving
3(15)
Inductive and Deductive Reasoning
18(10)
Scientific Notation and Estimation
28(23)
Chapter Summary
46(5)
The Nature of Sets
51(36)
Sets, Subsets, and Venn Diagrams
53(8)
Operations with Sets
61(6)
Applications of Sets
67(10)
Finite and Infinite Sets
77(10)
Chapter Summary
84(3)
The Nature of Logic
87(54)
Deductive Reasoning
89(8)
Truth Tables and the Conditional
97(9)
Operators and Laws of Logic
106(6)
The Nature of Proof
112(10)
Problem Solving Using Logic
122(9)
Logic Circuits
131(10)
Chapter Summary
136(5)
The Nature of Numeration Systems
141(40)
Early Numeration Systems
143(8)
Hindu--Arabic Numeration System
151(4)
Different Numeration Systems
155(6)
Binary Numeration System
161(5)
History of Calculating Devices
166(15)
Chapter Summary
177(4)
The Nature of Numbers
181(80)
Natural Numbers
183(8)
Prime Numbers
191(14)
Integers
205(8)
Rational Numbers
213(8)
Irrational Numbers
221(9)
Groups, Fields, and Real Numbers
230(12)
Discrete Mathematics
242(9)
Cryptography
251(10)
Chapter Summary
256(5)
The Nature of Algebra
261(82)
Polynomials
263(8)
Factoring
271(5)
Evaluation, Applications, and Spreadsheets
276(11)
Equations
287(8)
Guest Essay: Chaos
293(2)
Inequalities
295(5)
Algebra in Problem Solving
300(12)
Ratios, Proportions, and Problem Solving
312(9)
Percents
321(10)
Modeling Uncategorized Problems
331(12)
Chapter Summary
340(3)
The Nature of Geometry
343(62)
Geometry
345(10)
Polygons and Angles
355(9)
Triangles
364(7)
Similar Triangles
371(8)
Right-Triangle Trigonometry
379(8)
Mathematics, Art, and Non-Euclidean Geometries
387(18)
Chapter Summary
401(4)
The Nature of Networks and Graph Theory
405(42)
Euler Circuits and Hamiltonian Cycles
407(14)
Trees and Minimum Spanning Trees
421(12)
Topology and Fractals
433(14)
Guest Essay: What Good Are Fractals?
438(4)
Chapter Summary
442(5)
The Nature of Measurement
447(48)
Perimeter
449(9)
Area
458(10)
Surface Area, Volume, and Capacity
468(12)
Miscellaneous Measurements
480(11)
U.S.-Metric Conversions
491(4)
Chapter Summary
492(3)
The Nature of Growth
495(32)
Exponential Equations
497(9)
Logarithmic Equations
506(8)
Applications of Growth and Decay
514(13)
Chapter Summary
524(3)
The Nature of Financial Management
527(74)
Interest
529(15)
Installment Buying
544(9)
Sequences
553(13)
Series
566(11)
Annuities
577(7)
Amortization
584(8)
Summary of Financial Formulas
592(9)
Chapter Summary
596(5)
The Nature of Counting
601(36)
Permutations
603(8)
Combinations
611(8)
Counting Without Counting
619(9)
Rubik's Cube and Instant Insanity
628(9)
Chapter Summary
633(4)
The Nature of Probability
637(56)
Introduction to Probability
639(12)
Mathematical Expectation
651(9)
Probability Models
660(10)
Calculated Probabilities
670(13)
Guest Essay: Extrasensory Perception
680(3)
The Binomial Distribution
683(10)
Chapter Summary
689(4)
The Nature of Statistics
693(60)
Frequency Distributions and Graphs
695(14)
Descriptive Statistics
709(12)
The Normal Curve
721(11)
Correlation and Regression
732(8)
Sampling
740(13)
Chapter Summary
746(7)
The Nature of Graphs and Functions
753(46)
Cartesian Coordinates and Graphing Lines
755(10)
Graphing Half-Planes
765(2)
Graphing Curves
767(7)
Conic Sections
774(13)
Functions
787(12)
Chapter Summary
795(4)
The Nature of Mathematical Systems
799(58)
Systems of Linear Equations
801(5)
Problem Solving with Systems
806(11)
Matrix Solution of a System of Equations
817(11)
Inverse Matrices
828(15)
Modeling with Linear Programming
843(14)
Chapter Summary
853(4)
The Nature of Voting and Apportionment
857(60)
Voting
859(11)
Voting Dilemmas
870(18)
Apportionment
888(18)
Apportionment Paradoxes
906(11)
Chapter Summary
914(3)
The Nature of Calculus
917(2)
What Is Calculus?
919(10)
Limits
929(6)
Derivatives
935(11)
Integrals
946(7)
Chapter Summary
953
Epilogue: Why Not Math? Mathematics in the Natural Sciences, Social Sciences, and Humanities 1(1)
Appendix A Glossary 1(1)
Appendix B Selected Answers 1(1)
Index 1

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

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